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Use the substitution method to solve the system of equations. Choose the correct ordered pair.

[tex]\[
\begin{array}{l}
y = 3x - 4 \\
x = 9
\end{array}
\][/tex]

A. [tex]$(9, 23)$[/tex]

B. [tex]$(9, 31)$[/tex]

C. [tex]$(0, -4)$[/tex]

D. [tex]$(1, -1)$[/tex]

Sagot :

GinnyAnswer
To solve the system of equations using the substitution method, we begin with the two equations given:

[tex]\[ y = 3x - 4 \][/tex]
[tex]\[ x = 9 \][/tex]

Step 1: Identify the value of one variable from one of the equations. In this case, we already know that:
[tex]\[ x = 9 \][/tex]

Step 2: Substitute this value into the other equation. Substitute [tex]\( x = 9 \)[/tex] into the equation [tex]\( y = 3x - 4 \)[/tex]:
[tex]\[ y = 3(9) - 4 \][/tex]

Step 3: Simplify the right-hand side to find the value of [tex]\( y \)[/tex]:
[tex]\[ y = 27 - 4 \][/tex]
[tex]\[ y = 23 \][/tex]

Step 4: Write the ordered pair [tex]\((x, y)\)[/tex] using the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] we found:
[tex]\[ (x, y) = (9, 23) \][/tex]

Therefore, the correct ordered pair is:
[tex]\[ \boxed{(9, 23)} \][/tex]

So, the correct answer is:
[tex]\[ \text{A. } (9, 23) \][/tex]
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